Question

A 25-cm-long, center-fed, wire-type antenna is made of copper wire (nonmagnetic, σCu = 5.8×107 S/m) with a radius of 1 mm. The antenna is excited by a sinusoidal current with an amplitude I0 = 5 A. Determine the antenna gain (in db) and the time average power radiated, if the frequency is

(a) 1 MHz,
(b) 0.6 GHz.
(c) At what operating frequency the given antenna is more efficient and what is the ratio (in db) of powers emitted at 0.6 GHz and 1 MHz?

Answer 1

(a) 6.85 mw (b) 915 W (c) more efficient at higher frequencies

Step-by-step explanation:

(a) At 1 MHz

λ = c / f =
`3*10^8 / 10^6` = 300 m

λ / l = 300 / 0.25 = 1200, hence this is short dipole

From prad =
`40*pi^2*I0^2* ( l / λ)^2` - equation (I)

Solving for I0 = 5A,

we obtain prad = 6.85 mw

(b) At 0.6 GHz

Hence λ = c / f =
`3*10^8 / 0.6*10^9 = 1/2`

Likewise, substituting into equation (I)

prad = 915 w

(c) At higher frequency as seen in the previous two solutions, the antennae radiates 915/6.85 mw = 133500.8 times as much power as it does at lower frequency.

Hence, it is more efficient at higher operating frequency